Democratic Representations

Minimization of the $\ell_{\infty}$ (or maximum) norm subject to a constraint that imposes consistency to an underdetermined system of linear equations finds use in a large number of practical applications, including vector quantization, approximate nearest neighbor search, peak-to-average power ratio (or "crest factor") reduction in communication systems, and peak force minimization in robotics and control. This paper analyzes the fundamental properties of signal representations obtained by solving such a convex optimization problem. We develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, and study the efficacy of $\ell_{\infty}$-norm-based dynamic range reduction. Our analysis shows that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the computation of what we call democratic representations, whose entries all have small and similar magnitude, as well as low dynamic range. To compute democratic representations at low computational complexity, we present two new, efficient convex optimization algorithms. We finally demonstrate the efficacy of democratic representations for dynamic range reduction in a DVB-T2-based broadcast system.Comment: Submitted to a Journa

PAPR Reduction via Constellation Extension in OFDM Systems Using Generalized Benders Decomposition and Branch-and-Bound Techniques

In this paper, a novel constellation extension (CE)-based approach is presented to address the high peak-to-average power ratio (PAPR) problem at the transmitter side, which is an important drawback of orthogonal frequency-division multiplexing (OFDM) systems. This new proposal is formulated as a mixed-integer nonlinear programming optimization problem, which employs generalized Benders decomposition (GBD) and branch-and-bound (BB) methods to determine the most adequate extension factor and the optimum set of input symbols to be extended within a proper quarter plane of the constellation. The optimum technique based on GBD, which is denoted as GBD for constellation extension (GBDCE), provides a bound with relevant improvement in terms of PAPR reduction compared with other CE techniques, although it may exhibit slow convergence. To avoid excessive processing time in practical systems, the suboptimum BB for constellation extension (BBCE) scheme is proposed. Simulation results show that BBCE achieves a significant PAPR reduction, providing a good tradeoff between complexity and performance. We also show that the BBCE scheme performs satisfactorily in terms of power spectral density and bit error rate in the presence of a nonlinear high-power amplifier

Index modulation for next generation wireless communications.

Doctoral Degree. University of KwaZulu-Natal, Durban.A multicarrier index modulation technique in the form of quadrature spatial modulation (QSM) orthogonal frequency division multiplexing (QSM-OFDM) is proposed, in which transmit antenna indices are employed to transmit additional bits. Monte Carlo simulation results demonstrates a 5 dB gain in signal-to-noise ratio (SNR) over other OFDM schemes. Furthermore, an analysis of the receiver computational complexity is presented. A low-complexity near-ML detector for space-time block coded (STBC) spatial modulation (STBC-SM) with cyclic structure (STBC-CSM), which demonstrate near-ML error performance and yields significant reduction in computational complexity is proposed. In addition, the union-bound theoretical framework to quantify the average bit-error probability (ABEP) of STBC-CSM is formulated and validates the Monte Carlo simulation results. The application of media-based modulation (MBM), to STBC-SM and STBC-CSM employing radio frequency (RF) mirrors, in the form of MBSTBC-SM and MBSTBC-CSM is proposed to improve the error performance. Numerical results of the proposed schemes demonstrate significant improvement in error performance when compared with STBC-CSM and STBC-SM. In addition, the analytical framework of the union-bound on the ABEP of MBSTBC-SM and MBSTBC-CSM for the ML detector is formulated and agrees well with Monte Carlo simulations. Furthermore, a low-complexity near-ML detector for MBSTBC-SM and MBSTBC-CSM is proposed, and achieves a near-ML error performance. Monte Carlo simulation results demonstrate a trade-off between the error performance and the resolution of the detector that is employed. Finally, the application of MBM, an index modulated system to spatial modulation, in the form of spatial MBM (SMBM) is investigated. SMBM employs RF mirrors located around the transmit antenna units to create distinct channel paths to the receiver. This thesis presents an easy to evaluate theoretical bound for the error performance of SMBM, which is validated by Monte Carlo simulation results. Lastly, two low-complexity suboptimal mirror activation pattern (MAP) optimization techniques are proposed, which improve the error performance of SMBM significantly

Multicarrier Faster-than-Nyquist Signaling Transceivers: From Theory to Practice

The demand for spectrum resources in cellular systems worldwide has seen a tremendous escalation in the recent past. The mobile phones of today are capable of being cameras taking pictures and videos, able to browse the Internet, do video calling and much more than an yesteryear computer. Due to the variety and the amount of information that is being transmitted the demand for spectrum resources is continuously increasing. Efficient use of bandwidth resources has hence become a key parameter in the design and realization of wireless communication systems. Faster-than-Nyquist (FTN) signaling is one such technique that achieves bandwidth efficiency by making better use of the available spectrum resources at the expense of higher processing complexity in the transceiver. This thesis addresses the challenges and design trade offs arising during the hardware realization of Faster-than-Nyquist signaling transceivers. The FTN system has been evaluated for its achievable performance compared to the processing overhead in the transmitter and the receiver. Coexistence with OFDM systems, a more popular multicarrier scheme in existing and upcoming wireless standards, has been considered by designing FTN specific processing blocks as add-ons to the conventional transceiver chain. A multicarrier system capable of operating under both orthogonal and FTN signaling has been developed. The performance of the receiver was evaluated for AWGN and fading channels. The FTN system was able to achieve 2x improvement in bandwidth usage with similar performance as that of an OFDM system. The extra processing in the receiver was in terms of an iterative decoder for the decoding of FTN modulated signals. An efficient hardware architecture for the iterative decoder reusing the FTN specific processing blocks and realize different functionality has been designed. An ASIC implementation of this decoder was implemented in a 65nm CMOS technology and the implemented chip has been successfully verified for its functionality